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Erratum: The Robust Superreplication Problem: A dynamic Approach

SIAM JOURNAL ON FINANCIAL MATHEMATICS 2022年第2期13卷 653-655页

作者： Carassus, Laurence Obloj, Jan Wiesel, Johannes Leonard de Vinci Pole Univ Res Ctr F-92916 Paris France Univ Reims LMR UMR 9008 F-51100 Reims France Univ Oxford Math Inst Oxford OX1 3JP England Univ Oxford St Johns Coll Oxford OX1 3JP England Columbia Univ Stat Dept New York NY 10027 USA

The assertions of Proposition 3.7 in our paper ``The robust superreplication problem: A dynamic approach"" [L. Carassus, J. Ob\lo'\j, and J. Wiesel, SIAM J. Financial Math., 10 (2019), pp. 907--941] may ... 详细信息

关键词： robust pricing and hedging superhedging dynamic programming principle concave envelope dynamic robust approach

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Asset allocation under stochastic interest rate with regime switching

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ECONOMIC MODELLING 2012年第4期29卷 1126-1136页

作者： Shen, Yang Siu, Tak Kuen Macquarie Univ Dept Appl Finance & Actuarial Studies Fac Business & Econ Sydney NSW 2109 Australia

We investigate an optimal asset allocation problem in a Markovian regime-switching financial market with stochastic interest rate. The market has three investment opportunities, namely, a bank account, a share and a zero-coupon bond, where stochastic movements of the short rate and the share price are governed by a Markovian regime-switching Vasicek model and a Markovian regime-switching Geometric Brownian motion, respectively. We discuss the optimal asset allocation problem using the dynamic programming approach for stochastic optimal control and derive a regime-switching Hamilton-Jacobi-Bellman (HJB) equation. Particular attention is paid to the exponential utility case. Numerical and sensitivity analysis are provided for this case. The numerical results reveal that regime-switches described by a two-state Markov chain have significant impacts on the optimal investment strategies in the share and the bond. Furthermore, the market prices of risk in both the bond and share markets are crucial factors in determining the optimal investment strategies. (c) 2012 Elsevier B.V. All rights reserved.

关键词： Stochastic interest rate Regime-switching Stochastic flows dynamic programming principle HJB equation

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Restoration performance study of k-shortest disjoint paths in WDM optical networks

Restoration performance study of <i>k</i>-shortest disjoint ...

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14th International Conference on Computer Communications and Networks

作者： Tak, Sungwoo Park, E. K. Pusan Natl Univ Res Inst Comp Informat & Commun Dept Comp Sci & Engn Pusan 609735 South Korea Univ Missouri Sch Comp & Engn Kansas City MO 64110 USA

Many researchers have proposed restoration techniques incorporating the concept of k-shortest disjoint paths in survivable WDM (Wavelength Division Multiplexing) optical networks, but without considering network performance and network costs simultaneously. In this paper we need to carefully look into how well the concept of shortest disjoint paths is incorporated for given objective functions. Seven objective functions and four algorithms are presented to evaluate the concept of k-shortest disjoint paths for the design of a robust WDM optical network. A case study based on simulation experiments is conducted to illustrate the application and efficiency of k-shortest disjoint paths in terms of following objective goals: minimal wavelengths, minimal wavelength link distance, minimal wavelength mileage costs, even distribution of traffic flows, average restoration time of backup lightpaths, and physical topology constraints.

关键词： restoration shortest disjoint paths WDM optical networks optimization dynamic programming principle

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Optimal reinsurance policies with two reinsurers in continuous time

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ECONOMIC MODELLING 2016年第0期59卷 182-195页

作者： Meng, Hui Zhou, Ming Siu, Talc Kuen Cent Univ Finance & Econ China Inst Actuarial Sci Beijing 100081 Peoples R China Univ China Acad Sci Sch Management Beijing 100190 Peoples R China Macquarie Univ Fac Business & Econ Dept Appl Finance & Actuarial Studies Sydney NSW 2109 Australia

An optimal reinsurance problem of an insurer is studied in a continuous-time model, where insurance risk is partly transferred to two reinsurers, one adopting the expected-value premium principle and another one using the variance premium principle. The insurer aims to select an optimal reinsurance arrangement to minimize the probability of ruin. To provide an easy-to-implement solution to the problem, (semi)-explicit expressions for the optimal reinsurance strategies as well as the minimal ruin probabilities are derived for several claims distributions. Numerical studies including a real-data example based on the Danish fire insurance losses are provided to illustrate the solution of the problem. Our empirical results based on the Danish data reveal that the heavy-right-tailedness of claims distributions has a significant impact on the optimal reinsurance strategies and has a quite pronounced impact on the residual risk described by the minimal ruin probability. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Expected value premium principle Variance premium principle Ruin probability Proportional reinsurance Excess of loss reinsurance dynamic programming principle Heavy-tailed claims

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Neural networks for first order HJB equations and application to front propagation with obstacle terms

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PARTIAL DIFFERENTIAL EQUATIONS AND APPLICATIONS 2023年第5期4卷 1-36页

作者： Bokanowski, Olivier Prost, Averil Warin, Xavier Univ Paris Cite Lab Jacques Louis Lions LJLL F-75013 Paris France Sorbonne Univ CNRS LJLL F-75005 Paris France Normandie Univ INSA Rouen Normandie LMI UR 3226 F-76000 Rouen France EDF R&D F-91120 Palaiseau France FiME F-91120 Palaiseau France

We consider a deterministic optimal control problem, focusing on a finite horizon scenario. Our proposal involves employing deep neural network approximations to capture Bellman's dynamic programming principle. This also corresponds to solving first-order Hamilton-Jacobi-Bellman (HJB) equations. Our work builds upon the research conducted by Hur & eacute;et al. (SIAM J Numer Anal 59(1):525-557, 2021), which primarily focused on stochastic contexts. However, our objective is to develop a completely novel approach specifically designed to address error propagation in the absence of diffusion in the dynamics of the system. Our analysis provides precise error estimates in terms of an average norm. Furthermore, we provide several academic numerical examples that pertain to front propagation models incorporating obstacle constraints, demonstrating the effectiveness of our approach for systems with moderate dimensions (e.g., ranging from 2 to 8) and for nonsmooth value functions.

关键词： Neural networks Deterministic optimal control dynamic programming principle First order Hamilton-Jacobi-Bellman equation State constraints

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Data-driven surrogates of value functions and applications to feedback control for dynamical systems

Data-driven surrogates of value functions and applications t...

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9th Vienna International Conference on Mathematical Modelling (MATHMOD)

作者： Schmidt, A. Haasdonk, B. Univ Stuttgart Inst Appl Anal & Numer Simulat Pfaffenwaldring 57 D-70569 Stuttgart Germany

Dealing with high-dimensional feedback control problems is a difficult task when the classical dynamic programming principle is applied. Existing techniques restrict the application to relatively low dimensions since the discretizations typically suffer from the curse of dimensionality. In this paper we introduce a novel approximation technique for the value function of an infinite horizon optimal control. The method is based on solving optimal open loop control problems on a finite horizon with a sampling of the global value function along the generated trajectories. For the interpolation we choose a kernel orthogonal greedy strategy, because these methods are able to produce extreme sparse surrogates and enable rapid evaluations in high dimensions. Two numerical examples prove the performance of the approach and show that the method is able to deal with high-dimensional feedback control problems, where the dimensionality prevents the approximation by most existing methods. (C) 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： Kernel approximation optimal feedback control dynamic programming principle greedy techniques

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One Kind of Corporate International Optimal Investment and Consumption Choice Problem

One Kind of Corporate International Optimal Investment and C...

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27th Chinese Control Conference

作者： Huang Zongyuan Wu Zhen Shandong Univ Sch Math Jinan 250100 Peoples R China

ISBN: (纸本)9787900719706

In this paper, we study a the specific Hyperbolic Absolute Risk Aversion (HARA) case of corporate international optimal Portfolio and consumption choice problem. The investor can invest his wealth bond (bank account). On the other hand, he can invest his money to a real project with production in a foreign country. Using the celebrated dynamical programming principle method we provide the explicit optimal investment and consumption solution and give some simulation results to illustrates the influence of the volatility parameters on the optimal choice.

关键词： Investment Choice dynamic programming principle Hamilton-Jacobi-Bellman Equations

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Optimal multidimensional reinsurance policies under a common shock dependency structure

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EUROPEAN ACTUARIAL JOURNAL 2022年第2期12卷 559-577页

作者： Azarbad, M. Parham, G. A. Alavi, S. M. R. Shahid Chamran Univ Ahvaz Fac Math Sci & Comp Dept Stat Ahvaz Iran

In this paper, we consider an insurance company that is active in multiple dependent lines. We assume that the risk process in each line is a Cramer-Lundberg process. We use a common shock dependency structure to consider the possibility of simultaneous claims in different lines. According to a vector of reinsurance strategies, the insurer transfers some part of its risk to a reinsurance company. Our goal is to maximize our objective function (expected discounted surplus level integrated over time) using a dynamic programming method. The optimal objective function (value function) is characterized as the unique solution of the corresponding Hamilton-Jacobi-Bellman equation with some boundary conditions. Moreover, an algorithm is proposed to numerically obtain the optimal solution of the objective function, which corresponds to the optimal reinsurance strategies.

关键词： Cramer-Lundberg process Common shock dynamic programming principle Reinsurance

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Stochastic modeling and control of bioreactors

Stochastic modeling and control of bioreactors

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20th World Congress of the International-Federation-of-Automatic-Control (IFAC)

作者： Fontbona, J. Ramirez, H. C. Riquelme, V. Silva, F. J. Univ Chile Dept Ingn Matemat Beauchef 851Casilla 170-3 Santiago 3 Chile Univ Chile CNRS Ctr Modelamiento Matemat UMI 2807 Beauchef 851Casilla 170-3 Santiago 3 Chile Univ Limoges Fac Sci & Tech UMR CNRS 7252 Inst Rech XLIM DMI F-87060 Limoges France

In this work we propose a stochastic model for a sequencing-batch reactor (SBR) and for a chemostat. Both models are described by systems of Stochastic Differential Equations (SDEs), which are obtained as limits of suitable Markov Processes characterizing the microscopic behavior. We study the existence of solutions of the obtained equations as well as some properties, among which the possible extinction of the biomass is the most remarkable feature. The implications of this behavior are illustrated in the problem consisting in maximizing the probability of reaching a desired depollution level prior to biomass extinction. (C) 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： Chemostat SBR demographic stochasticity Stochastic Control dynamic programming principle

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The Corporate Optimal Portfolio and Consumption Choice Problem in Trade Project with Borrowing Rate Higher than Deposit Rate 38

The Corporate Optimal Portfolio and Consumption Choice Probl...

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38th Chinese Control Conference (CCC)

作者： Zhang, Panpan Shandong Univ Sch Control Sci & Engn Jinan 250061 Peoples R China

ISBN: (纸本)9789881563972

This paper is concerned with a kind of optimal portfolio and consumption choice problem, where an investor can invest his wealth in a trade project and foreign exchange deposit. The trade project earns profit by buying the merchandise and selling it with a higher price. The bank pays at an interest rate for any deposit, and vice takes at a large rate for any loan. The optimal strategy is obtained by Hamilton-Jacobi-Bellman (HJB) equation, which is derived from dynamic programming principle. For the specific Hyperbolic Absolute Risk Aversion (HARA) case, we get the explicit form of optimal portfolio and consumption solution, and we give some simulation results.

关键词： Consumption/Investment Optimization dynamic programming principle HJB Equation HARA

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